Overview¶
We model one of the most complex systems: the human brain
Great number of neurons and enormous number of dendrons
Overview¶
Self organised network:
- Mashed rat brains
- Kept alive in petridishes
- Small-world networks grow naturally
Model¶
Random graph:
- Number of nodes
- Relatively high number of edges
- Assign random activation value $[-1, 1]$
Model¶
Iteratively update graph:
- Apply logistic map
- Randomly select pivot
- Find candidate and outcast
- Rewire if possible
Model¶
1 - Apply logistic map¶
Each nodes activation value is updated according to the equation below
$$
\begin{equation*} x^i_{n+1} = (1- \epsilon) \cdot f(x^j_n)+\frac{\epsilon}{M_i}\sum_{j \in B(i)}f(x^j_n) \end{equation*}$$
Where
$$f(x) = 1 - a x^2$$
Epsilon is the coupling parameter
a is a constant in the logistic map
In [3]:
plt.scatter(a,e)
plt.title("Parameter space")
plt.xlabel("a")
plt.ylabel("epsilon")
plt.grid()
plt.show()
In [4]:
init_notebook_mode(connected=True)
figure = build_fig()
iplot(figure, validate = False)